“Congressman Jim Bridenstine said on Monday he is pleased to know that Dr. Coburn is not resigning strictly on health concerns. Bridenstine said he is honored by the number of people, statewide and nationally, encouraging him to run for the Senate seat, but he is not inclined to rush the decision,” the statement, obtained first by The Hill, reads.

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The campaign’s assertion that numerous supporters are encouraging him to enter the race runs counter to suggestions that Bridenstine may be getting cold feet and discouragement from Oklahoma conservatives on the race.

He’s seen by national conservatives as the best alternative to Rep. James Lankford (R-Okla.), who announced his decision to run on Monday and was immediately met with conservative pushback.

One national conservative group, the Madison Project, urged Bridenstine to jump into the race, saying he “has too much to offer Oklahoma in the Senate for him to sit this one out.”

Another, the Senate Conservatives Fund, suggested in endorsing him for reelection last year that he would make a good Senate candidate in the future. The congressman would likely get the support of both groups if he ran for the seat.

A source close to Bridenstine said his decision is likely to come within the week.

But another potential candidate, Oklahoma House Speaker T.W. Shannon, could complicate Bridenstine’s bid if he decided to run.

A source close to Shannon tells The Hill that he’s looking very closely at the race. He would compete with Bridenstine for conservatives, and potentially hand Lankford the nomination, if the two split the conservative vote.

In a Monday statement, Shannon said he's "disappointed" that Coburn is stepping down, but hasn't yet made his own decision on the race.

"I have enormous respect and admiration for Dr. Coburn and his service to our country, and, like most Oklahomans, I am disappointed that he will be leaving the United States Senate," he said.

"No one can replace Tom Coburn, but someone will succeed him. I am praying with my family about whether to enter the race to do just that, and I know the Lord will clearly place on my heart what my assignment is," Shannon added.

The race could, however, head to a runoff, if no candidate in a three-way primary were able to get a majority of the votes, and Bridenstine’s supporters privately express confidence in his chances in such a scenario.

Coburn announced last Thursday that, due partly to health concerns, he's cutting his current term short and retiring at the end of this year, sparking a special election for his seat, the dates of which will coincide with this year's regularly scheduled elections.